Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2018, Article ID 1730149, 15 pages
Research Article

Detecting Activation in fMRI Data: An Approach Based on Sparse Representation of BOLD Signal

1Department of Mathematics and Physics, Bioengineering Group, UNET, San Cristóbal, Venezuela
2Research Center for Biomedical Engineering and Telemedicine, Electrical Engineering Department, ULA, Mérida, Venezuela
3Computer Science Department, Universidad de Cuenca, Cuenca, Ecuador

Correspondence should be addressed to Blanca Guillen; moc.liamg@nelliugalb

Received 29 August 2017; Accepted 3 January 2018; Published 15 February 2018

Academic Editor: Roberto Fedele

Copyright © 2018 Blanca Guillen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a simple yet effective approach for detecting activated voxels in fMRI data by exploiting the inherent sparsity property of the BOLD signal in temporal and spatial domains. In the time domain, the approach combines the General Linear Model (GLM) with a Least Absolute Deviation (LAD) based regression method regularized by the pseudonorm to promote sparsity in the parameter vector of the model. In the spatial domain, detection of activated regions is based on thresholding the spatial map of estimated parameters associated with a particular stimulus. The threshold is calculated by exploiting the sparseness of the BOLD signal in the spatial domain assuming a Laplacian distribution model. The proposed approach is validated using synthetic and real fMRI data. For synthetic data, results show that the proposed approach is able to detect most activated voxels without any false activation. For real data, the method is evaluated through comparison with the SPM software. Results indicate that this approach can effectively find activated regions that are similar to those found by SPM, but using a much simpler approach. This study may lead to the development of robust spatial approaches to further simplifying the complexity of classical schemes.